Seminars in the next week

Oct 26 (Tue)

13:00 Sacha Mangerel: * Gaussian distribution of squarefree and B-free numbers in short intervals *

(Joint with O. Gorodetsky and B. Rodgers) It is a classical quest in analytic number theory to understand the fine-scale distribution of arithmetic sequences such as the primes. For a given length scale h, the number of elements of a "nice" sequence in a uniformly randomly selected interval (x,x+h], 1 ≤ x ≤ X, is expected to follow the statistics of a normally distributed random variable (in suitable ranges of 1 ≤ h ≤ X). Following the work of Montgomery and Soundararajan, this is known to be true for the primes, but only if we assume several deep and long-standing conjectures such as the Riemann Hypothesis. In fact, previously such distributional results had not been proven for any sequence of number-theoretic interest, unconditionally.
As a model for the primes, in this talk I will address such statistical questions for the sequence of squarefree numbers, i.e., numbers not divisible by the square of any prime, among other related "sifted" sequences called B-free numbers. I hope to further motivate and explain our main result that shows, unconditionally, that short interval counts of squarefree numbers do satisfy Gaussian statistics, answering several old questions of R.R. Hall.

**Venue:** (unless stated above) MCS3070

Oct 28 (Thu)

13:00 Ximena Fernández: * Morse theory for group presentations *

The Andrews-Curtis conjecture (1965) is one the most relevant open problems in low-dimensional topology, closely related to the Whitehead asphericity conjecture, the Zeeman conjecture and the smooth Poincaré conjecture. It states that any contractible 2-dimensional CW-complex 3-deforms to a point. Its algebraic equivalent formulation states that any balanced presentation of the trivial group can be transformed into the empty presentation through a sequence of a class of movements (called Q**-transformations) that do not change its deficiency.
In this talk, I will introduce a new combinatorial method to study Q**-transformations of group presentations or, equivalently, 3-deformations of CW-complexes. The procedure is based on a refinement of discrete Morse theory in terms of Whitehead deformations. I will apply this technique to show that some known potential counterexamples to the Andrews-Curtis conjecture do satisfy the conjecture. Preprint: https://arxiv.org/abs/1912.00115

14:00 Madalena Lemos: * Bootstrapping strongly coupled (super)conformal field theories *

Symmetries have frequently aided our study of physical systems. For conformally invariant quantum field theories there has been a lot of recent progress in what can be broadly described as "bootstrapping" these theories from their symmetries. I will review this progress and how it can be used to learn about strongly coupled theories, for which we often cannot rely on traditional perturbative methods, with a special focus on supersymmetric conformal field theories.
Zoom: https://durhamuniversity.zoom.us/j/96642285471?pwd=OU5XVVVKSzhEczVTSHBzb25PWlk2Zz09

**Venue:** (unless stated above) OC218

Oct 29 (Fri)

13:00 Lucia Scardia: * Nonlocal anisotropic energy-driven pattern formation *

Nonlocal energies are continuum models for large systems of particles with long-range interactions. Under the assumption that the interaction potential is radially symmetric, several authors have investigated qualitative properties of energy minimisers. But what can be said in the case of anisotropic kernels? Motivated by the example of dislocation interactions in materials science, we pushed the methods developed for nonlocal energies beyond the case of radially symmetric potentials, and discovered surprising connections with random matrices, fluid dynamics, and Calderón-Zygmund operators.

13:00 Matthew Buican: * Some Galois Actions in Topological Quantum Field Theory *

Galois theory features prominently in many areas of modern mathematics. Although somewhat less appreciated, interesting (and useful) Galois groups sometimes lurk beneath the surface in physics as well. One particularly fruitful area for studying physical Galois actions is in the context of TQFT and topological phases of matter. With this in mind, we will discuss some applications of Galois theory to the study of the symmetries and structures present in 2+1 dimensional TQFT.

Nov 01 (Mon)

13:00 Victoria Volodina: * tbc *

tbc

**Venue:** (unless stated above) MCS2068

14:00 Anne Schreuder: * On Lévy-driven Loewner Evolutions *

This talk is about the behaviour of Loewner evolutions driven by a Lévy process. Schramm's celebrated version (Schramm-Loewner evolution), driven by standard Brownian motion, has been a great success for describing critical interfaces in statistical physics. Loewner evolutions with other random drivers have been proposed, for instance, as candidates for finding extremal multifractal spectra, and some tree-like growth processes in statistical physics. Questions on how the Loewner trace behaves, e.g., whether it is generated by a (discontinuous) curve, whether it is locally connected, tree-like, or forest-like, have been partially answered in the symmetric alpha-stable case. We consider the case of general Levy drivers. Joint work with Eveliina Peltola (Bonn and Helsinki).

**Venue:** (unless stated above) MCS2068

Click on title to see abstract (and venue, if in person). Zoom links, if available, are given for today's seminars only.

Seminar Series

(Click on series to expand.)
Contact: megan.k.griffin-pickering@durham.ac.uk

Oct 29 13:00 Lucia Scardia: * Nonlocal anisotropic energy-driven pattern formation *

Nonlocal energies are continuum models for large systems of particles with long-range interactions. Under the assumption that the interaction potential is radially symmetric, several authors have investigated qualitative properties of energy minimisers. But what can be said in the case of anisotropic kernels? Motivated by the example of dislocation interactions in materials science, we pushed the methods developed for nonlocal energies beyond the case of radially symmetric potentials, and discovered surprising connections with random matrices, fluid dynamics, and Calderón-Zygmund operators.

Nov 05 12:00 Csaba Farkas: * tba *

tba

Nov 12 13:00 Klemens Fellner: * tba *

tba

Nov 19 13:00 Pierre Degond: * Body orientation dynamics *

Collective dynamics has stimulated intense mathematical research in the last decade. Many different models have been proposed but most of them rely on describing agents as point particles in position-velocity space. We propose a model where the particles carry more complex geometric structure. Specifically, the particles are rigid bodies whose attitude (or body orientation) is described by an orthonormal frame. Particles tend to align their frame with those of their neighbours. In this talk we will review recent results on this model which are issued from collaborations with Antoine Diez, Amic Frouvelle, Sara Merino-Aceituno, Mingye Na and Ariane Trescases.

Dec 10 13:00 Alexandru Kristaly: * tba *

tba

Contact: christopher.prior@durham.ac.uk

No upcoming seminars have been scheduled (not unusual during summer breaks).

Usual Venue: MCS3070

Contact: jack.g.shotton@durham.ac.uk

Oct 26 13:00 Sacha Mangerel: * Gaussian distribution of squarefree and B-free numbers in short intervals *

(Joint with O. Gorodetsky and B. Rodgers) It is a classical quest in analytic number theory to understand the fine-scale distribution of arithmetic sequences such as the primes. For a given length scale h, the number of elements of a "nice" sequence in a uniformly randomly selected interval (x,x+h], 1 ≤ x ≤ X, is expected to follow the statistics of a normally distributed random variable (in suitable ranges of 1 ≤ h ≤ X). Following the work of Montgomery and Soundararajan, this is known to be true for the primes, but only if we assume several deep and long-standing conjectures such as the Riemann Hypothesis. In fact, previously such distributional results had not been proven for any sequence of number-theoretic interest, unconditionally.
As a model for the primes, in this talk I will address such statistical questions for the sequence of squarefree numbers, i.e., numbers not divisible by the square of any prime, among other related "sifted" sequences called B-free numbers. I hope to further motivate and explain our main result that shows, unconditionally, that short interval counts of squarefree numbers do satisfy Gaussian statistics, answering several old questions of R.R. Hall.

Nov 09 13:00 Rachel Newton: * TBC *

TBC

Nov 23 15:00 Aled Walker: * TBC *

TBC

Nov 30 13:00 Hanneke Wiersema: * TBC *

TBC

Dec 07 13:00 Mehmet Haluk Şengün: * TBC *

TBC

Usual Venue: OC218

Contact: stefano.cremonesi@durham.ac.uk

For more information, see HERE.

Oct 28 14:00 Madalena Lemos: * Bootstrapping strongly coupled (super)conformal field theories *

Symmetries have frequently aided our study of physical systems. For conformally invariant quantum field theories there has been a lot of recent progress in what can be broadly described as "bootstrapping" these theories from their symmetries. I will review this progress and how it can be used to learn about strongly coupled theories, for which we often cannot rely on traditional perturbative methods, with a special focus on supersymmetric conformal field theories.
Zoom: https://durhamuniversity.zoom.us/j/96642285471?pwd=OU5XVVVKSzhEczVTSHBzb25PWlk2Zz09

Nov 11 14:10 Suchita Kulkarni: * TBA *

Nov 25 14:00 Mohamed Anber: * TBA *

Dec 09 14:00 Bobby Acharya: * TBA *

Feb 03 14:00 Djuna Croon: * TBA *

Mar 03 14:00 Luigi Del Debbio: * TBA *

Contact: hugo.fortin@durham.ac.uk

No upcoming seminars have been scheduled (not unusual during summer breaks).

Contact: p.e.dorey@durham.ac.uk

No upcoming seminars have been scheduled (not unusual during summer breaks).

Contact: fernando.galaz-garcia@durham.ac.uk

Recordings of past seminars can be found HERE.

Oct 28 13:00 Ximena Fernández: * Morse theory for group presentations *

The Andrews-Curtis conjecture (1965) is one the most relevant open problems in low-dimensional topology, closely related to the Whitehead asphericity conjecture, the Zeeman conjecture and the smooth Poincaré conjecture. It states that any contractible 2-dimensional CW-complex 3-deforms to a point. Its algebraic equivalent formulation states that any balanced presentation of the trivial group can be transformed into the empty presentation through a sequence of a class of movements (called Q**-transformations) that do not change its deficiency.
In this talk, I will introduce a new combinatorial method to study Q**-transformations of group presentations or, equivalently, 3-deformations of CW-complexes. The procedure is based on a refinement of discrete Morse theory in terms of Whitehead deformations. I will apply this technique to show that some known potential counterexamples to the Andrews-Curtis conjecture do satisfy the conjecture. Preprint: https://arxiv.org/abs/1912.00115

Nov 04 13:00 Nelia Charalambous: * The form spectrum of open manifolds *

The computation of the essential spectrum of the Laplacian requires the construction of a large class of test differential forms. On a general open manifold this is a difficult task, since there exists only a small collection of canonically defined differential forms to work with. In our work with Zhiqin Lu, we compute the essential k-form spectrum over asymptotically flat manifolds by combining two methods: First, we introduce a new version of the generalized Weyl criterion, which greatly reduces the regularity and smoothness of the test differential forms; second, we make use of Cheeger-Fukaya-Gromov theory and Cheeger-Colding theory to obtain a new type of test differential forms at the ends of the manifold. The generalized Weyl criterion can also be used to obtain other interesting facts about the k-form essential spectrum over an open manifold. Finally, we present some recent results on the form spectrum of negatively curved manifolds.

Nov 11 13:00 Patrick Orson: * TBA *

TBA

Nov 18 13:05 Norbert Peyerimhoff: * TBA *

TBA

Dec 02 13:00 Jian Ge: * TBA *

TBA

Dec 09 13:00 Wilderich Tuschmann: * TBA *

TBA

Jan 13 13:00 Annegreat Burtscher: * TBA *

TBA

Jan 20 13:00 Jesús Núñez-Zimbrón: * TBA *

TBA

Feb 03 13:00 Ana Lucia Garcia Pulido: * TBA *

TBA

Contact: inaki.garcia-etxebarria@durham.ac.uk

Note: if held in person (please see abstract), the usual room is MCS2068; otherwise on zoom.

Oct 29 13:00 Matthew Buican: * Some Galois Actions in Topological Quantum Field Theory *

Galois theory features prominently in many areas of modern mathematics. Although somewhat less appreciated, interesting (and useful) Galois groups sometimes lurk beneath the surface in physics as well. One particularly fruitful area for studying physical Galois actions is in the context of TQFT and topological phases of matter. With this in mind, we will discuss some applications of Galois theory to the study of the symmetries and structures present in 2+1 dimensional TQFT.

Nov 05 13:00 Phil Saad: * TBA *

Nov 12 13:00 Chris Elliott: * TBA *

Nov 19 13:00 Jackson Fliss: * TBA *

Nov 26 13:00 Lorenzo Di Pietro: * TBA *

Usual Venue: MCS2068

Contact: ellen.g.powell@durham.ac.uk

Nov 01 14:00 Anne Schreuder: * On Lévy-driven Loewner Evolutions *

This talk is about the behaviour of Loewner evolutions driven by a Lévy process. Schramm's celebrated version (Schramm-Loewner evolution), driven by standard Brownian motion, has been a great success for describing critical interfaces in statistical physics. Loewner evolutions with other random drivers have been proposed, for instance, as candidates for finding extremal multifractal spectra, and some tree-like growth processes in statistical physics. Questions on how the Loewner trace behaves, e.g., whether it is generated by a (discontinuous) curve, whether it is locally connected, tree-like, or forest-like, have been partially answered in the symmetric alpha-stable case. We consider the case of general Levy drivers. Joint work with Eveliina Peltola (Bonn and Helsinki).

Nov 08 14:00 Mo Dick Wong: * tbc *

tbc

Nov 15 14:00 Vadim Shcherbakov : * tbc *

tbc

Nov 22 14:00 Travis Scrimshaw: * tbc *

tbc

Nov 29 14:00 Lukas Schoug: * tbc *

tbc

Dec 06 14:00 Sigurður Örn Stefánsson : * tbc *

tbc

Usual Venue: MCS0001

Contact: jack.g.shotton@durham.ac.uk

Nov 08 13:00 Fernando Galaz-Garcia: * TBC *

TBC

Nov 15 13:00 Rhiannon Dougall: * TBC *

TBC

Nov 22 13:00 Irene Pasquinelli: * TBC *

TBC

Nov 29 13:00 Jeffrey Giansiracusa: * TBC *

TBC

Usual Venue: MCS2068

Contact: georgios.karagiannis@durham.ac.uk, konstantinos.perrakis@durham.ac.uk

Nov 01 13:00 Victoria Volodina: * tbc *

tbc

Nov 22 13:00 Chris Sherlock: * tbc *

tbc

Contact: kieran.f.richards@durham.ac.uk

No upcoming seminars have been scheduled (not unusual during summer breaks).